RC Filter Calculator — Cutoff Frequency & Time Constant
Find the cutoff (−3 dB) frequency, time constant and magnitude response of a first-order RC low-pass or high-pass filter from the resistor and capacitor values.
Ω
µF
Filter type
Output amplitude is 70.7% of input (−3 dB) at this frequency
- 1
Time constant τ = R × C
10,000 × 0.1 µF × 10⁻⁶ = 0.001Product of resistance (Ω) and capacitance converted to farads. - 2
Cutoff frequency
1 ÷ (2π × 0.001) = 159.15
How does this calculator work?
An RC filter's cutoff frequency is f_c = 1/(2π·R·C): the point where output amplitude drops to 70.7% (−3 dB) of input. The time constant τ = R·C sets response speed. For R = 10 kΩ and C = 0.1 µF, f_c ≈ 159 Hz and τ = 1 ms — frequencies above 159 Hz are attenuated in a low-pass configuration.
Formula
How this is calculated
A first-order RC filter is built from a resistor and a capacitor in series. For a low-pass filter the output is taken across the capacitor; for high-pass it is taken across the resistor. Both share the same cutoff (corner) frequency f_c = 1/(2π·R·C) — the point at which the output power drops to half (−3 dB), or equivalently where the output amplitude falls to 1/√2 ≈ 70.7% of the input. Below f_c a low-pass filter passes signals with little loss; above it the gain rolls off at −20 dB per decade of frequency.
The time constant τ = R·C (in seconds) is the reciprocal of the angular cutoff frequency: ω_c = 1/τ = 2π·f_c. It also describes the transient response: after one time constant, the capacitor voltage rises to ~63.2% of its final value following a step input. A larger RC product means a lower cutoff frequency and slower response. The phase shift at f_c is exactly −45° for low-pass and +45° for high-pass.
This model assumes an ideal first-order RC filter — zero-impedance source, infinite-impedance load, and ideal components. Real components carry tolerances (typically ±5–10% for resistors, ±10–20% for capacitors), parasitic inductance, and loading effects that shift the actual cutoff. For sharper roll-offs, second- or higher-order active (op-amp) filter designs are used.
Frequently asked questions
At the cutoff frequency the output power is half the input power (−3 dB), and the output voltage amplitude is 1/√2 ≈ 70.7% of the input. It marks the boundary between the filter's pass band and its stop band — signals well below f_c pass nearly unchanged through a low-pass filter; signals above f_c are progressively attenuated at 20 dB per frequency decade.
Rearrange the formula: R·C = 1/(2π·f_c). Fix one component to a standard value (e.g. C = 100 nF = 0.1 µF) and solve for the other: R = 1/(2π × f_c × C). Round to the nearest standard E-series resistor value, then verify with this calculator.
At f = f_c the capacitive reactance equals the resistance (X_C = R), so the phasor diagram forms an isosceles right triangle with equal real and imaginary parts — giving exactly 45° of phase lag for a low-pass filter. Below f_c the phase approaches 0°; above f_c it approaches −90°.
Also known as
TG we-Calculate Editorial Team. (2026). RC Filter Calculator — Cutoff Frequency & Time Constant [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rc-filter-calculator
TG we-Calculate Editorial Team. "RC Filter Calculator — Cutoff Frequency & Time Constant." TG we-Calculate. 2026. https://we-calculate.com/calculator/rc-filter-calculator.
TG we-Calculate Editorial Team, "RC Filter Calculator — Cutoff Frequency & Time Constant," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rc-filter-calculator
@misc{wecalculate_rc_filter_calculator, title = {RC Filter Calculator — Cutoff Frequency & Time Constant}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rc-filter-calculator}}, year = {2026}, note = {TG we-Calculate} }
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